Concerning The Minecraft Skybox

Question

I was wondering how does the stars in night time in minecraft work, are they point sprites? And are they placed on a texture or just randomly placed on some far away location.

EDIT 1:

OK, well, with the imformation gathered concerning the minecraft skybox I now know that the stars are not directly textured onto a sphere but are individial quads placed some set distance (the radius of the sphere) from the player.

The problem is now I will I go about getting a random position on that sphere (not in it and not too far out of it). And how will I get rotation for it to face the player? One user suggested normalising a random Vector3 then multiplying it by the spheres radius which I think, simply won't work. Also another suggested that I use the formular: "1 = x^2+y^2+z^2", I don't know how I would use this to find a random position on a sphere either.

EDIT 2:

OK, I haven't tested this or anything but from all the imformation gathered from PrinceCharles anwser it should be something like this:

            float x = (float)random.NextDouble() * 2 - 1;
            float y = (float)random.NextDouble() * 2 - 1;
            float z = (float)Math.Sqrt((double)(1f - x * x - y * y));

            Vector3 randomPoint = new Vector3(x, y, z);

            if (randomPoint.Length() != 0)
            {
                randomPoint.Normalize();
                Vector3 pointOnSphere = randomPoint * radius;

                                  // Position     Rotation
                stars.Add(new Star(pointOnSphere, new Vector3(0, 0, 0)));
            }

The reason for the "* 2 - 1" is to give the random a range of -1 to 1. I think that is correct...

EDIT 3:

One side of the map:

The other:

Any ideas?

Thanks :)

Answer 1

You want hemisphere point picking, which is not trivial to get right.

It is incorrect to pick uniform x, y and z coordinates and normalise them.

It is also incorrect to pick uniform angle values.

I believe the less computationally expensive method is derived from Marsaglia’s sphere point picking algorithm:

float x1, x2, p, q;
do
{
    x1 = (float)random.NextDouble() * 2.0f - 1.0f;
    x2 = (float)random.NextDouble() * 2.0f - 1.0f;
    p = x1 * x1 + x2 * x2;
} while (p > 1.0f);
q = 2.0f * sqrt(1.0f - p);

return Vector3(x1 * q, x2 * q, abs(1.0f - 2.0f * p));

Note: if you get rid of the abs() you get full sphere picking, which might be useful, too.

Answer 2

They're not point sprites because of:

• Minecraft doesn't used GLSL, and you can't easily do variable sized (or rotated) point sprites without shaders.

• Point sprites can't be partially clipped at the edge of a screen, while Minecraft's stars can be.

They're just boring old white polygons placed camera facing as if on the inside of a sphere with a bit of blending. Nice effect.

Answer 3

Probably just part of your question:

The mathematical definition of a unit sphere (e.g. 1 unit radius) is 1 = x² + y² + z²

Therefore to find a random point on a sphere you can choose any two of the variables in that equation and calculate the third. What's important here is, that x,y,z must be in the range of -1 to 1 - As mentioned the sphere has radius 1.

So lets say i randomly chose x = 0.5 and y = -0.75 then to calculate z we have to solve:
z = SQRT(1 - x² - y²)
z = SQRT(1 - 0.5² - 0.75²)
z = SQRT(1 - 0.25 - 0.5625)
z = SQRT(0.1875)
z = 0.4330

This vector (0.5, 0.75, 0.433) lies on a sphere with radius 1 and can then be multiplied by any scaling factor to get a point on a bigger/smaller sphere.

Hope that helps!

EDIT 1:

I haven't tested this either but from what Kevin Reid and BiAiB mentioned this will give you a uniformed distribution (over a whole sphere):

        float x = (float)random.NextDouble() * 2 - 1;
        float y = (float)random.NextDouble() * 2 - 1;
        float z = (float)random.NextDouble() * 2 - 1;

        Vector3 randomPoint = new Vector3(x, y, z);
        if(randomPoint.Length() != 0)
          Vector3 pointOnSphere = randomPoint.Normalize();

To find a point on a half sphere (depending on your orientation of the world) choose one coordinate from 0 to 1:

        float z = (float)random.NextDouble();

To get a bigger/smaller sphere multiply the Vector3 with the desired sphereRadius

          Vector3 pointOnSphere = randomPoint.Normalize() * sphereRadius;